Statistical analysis of Boolean models with randomly scaled grains. (English. Ukrainian original) Zbl 0840.62087

Molchanov, I. S.

Theory Probab. Math. Stat. 48, 105-110 (1994); translation from Teor. Jmovirn. Mat. Stat. 48, 147-154 (1993).

Summary: The stationary Boolean model with a grain \(\xi M\), where \(M\) is a non-random centrally symmetric convex set, is considered. Certain consistent estimates for the moments and distribution of the random variable \(\xi\) are given. The estimation is based on the notion of empirical moving functional of a random closed set and the Glivenko-Cantelli theorem for random closed sets.

MSC:

62M99	Inference from stochastic processes
62G05	Nonparametric estimation
60D05	Geometric probability and stochastic geometry

Keywords:

stationary Poisson point process; non-random centrally symmetric convex set; random closed sets; stationary Boolean model; grain; consistent estimates; moments; empirical moving functional; Glivenko-Cantelli theorem